Epitaxial strain

The PbTi03 films were grown epitaxially on SrTiOs (001) substrates as described previously [2], Cation precursors were either titanium isopropoxide (tip) or titanium tertbutoxide (ttb), and tetraethyl lead (tel). The oxidant was O2, with N2 carrier gas. Films were typically deposited at 750°C at a total pressure of 10 Torr (P02 = 2.5 Torr). Under appropriate growth conditions, the PbTi03 films replicated the high crystalline quality of the substrates (0.01° typical mosaic). Films thinner than 40 nm remained lattice matched with the SrTiC>3, while the epitaxial strain was mostly relaxed in thicker films. 

A primary focus of our work has been to understand the ferroelectric phase transition in thin epitaxial films of PbTiOs. It is expected that epitaxial strain effects are important in such films because of the large, anisotropic strain associated with the phase transition. Figure 8.3 shows the phase diagram for PbTiOs as a function of epitaxial strain and temperature calculated using Landau-Ginzburg-Devonshire (lgd) theory [9], Here epitaxial strain is defined as the in-plane strain imposed by the substrate, experienced by the cubic (paraelectric) phase of PbTiOs. The dashed line shows that a coherent PbTiOs film on a SrTiOs substrate experiences somewhat more than 1 % compressive epitaxial strain. Such compressive strain favors the ferroelectric PbTiOs phase having the c domain orientation, i.e. with the c (polar) axis normal to the film. From Figure 8.3 one can see that the paraelectric-ferroelectric transition temperature Tc for coherently-strained PbTiOs films on SrTiOs is predicted to be elevated by 260°C above that of... 

Figure 8.3 Phase diagram for epitaxially-strained PbTiOs calculated using Landau-Ginzburg-Devonshire theory [9]. The dashed line shows the epitaxial strain corresponding to a SrTiC>3...

The preceding bandgap values are given for low (2 - 10 K) temperature (T). Of primary importance is the temperature dependence of the bandgaps, in particular their value at room temperature (RT). From the previous discussion, different T dependencies are expected, due to the different strain state of the samples studied. For GaN on sapphire, both the residual epitaxial strain and the thermoelastic strain are compressive, whereas for GaN on SiC, the thermoelastic part of the residual strain is tensile. This leads to very different temperature dependencies between low T and RT, as shown in FIGURE 1. Note that results different from those shown on FIGURE 1 have also been reported [8],... 

Renewed interest in the superconductivity of cuprate films was generated by the observation that T for an epitaxial film of Lai,9Sro,iCu04 deposited on SrLaA104 was 49 K, roughly double the bulk value of 25 K. The increase was initially attributed to the effects of compressive epitaxial strain. ... 

In such cases a local-equilibrium structure may be obtained theoretically by minimization of the free energy of the system under the constraint of a fixed alloy composition in the surface region [8,17-24]. Although this approach is very similar to the one used for bulk systems, it should be modified due to the specific features introduced by the surface. First of all, since the structure of the underlying bulk system is fixed, it acts as the source of an external field for the surface alloy, creating, for instance, epitaxial strain. Secondly, since the surface is an open system, it allows the formation of a great variety of different structures, which may not have any connection at all to the crystal structure of the substrate. Finally, the surface is a spatially inhomogeneous system, and thus different alloy components have their own... 

Another factor which may change the alloying at the surface is the epitaxial strain of the surface alloy due to its pseudomorphic attachment to the substrate. This concerns especially systems with elements that differ considerably in size... 

In this section we have considered examples of systems where the alloy behavior on the surface remains the same as in the bulk. As has been mentioned this is basically due to the fact that the size of the alloy components is practically the same. On the other hand, it is now well-known that alloying behavior on surfaces may change due epitaxial strain of the surface alloy [38] when the alloy components have different sizes. Such an alloying in this case is simply a consequence of the release of the epitaxial strain energy, which is positive and reaches its maximal value for an overlayer of a pure deposited element on the substrate. 

Eq.(5) describes the nonlinear evolution of a thin, epitaxially-strained film in the presence of wetting interactions with the substrate. Without wetting interactions g = 0), the dispersion relation for the growth rate of infinitesimal perturbations of the film surface h isa = k —k, see Fig.2a (in the... 

The presence of the zero mode, as well as the presence of the quadratic nonlinear terms with the coefficients ri and f2 in eqs. (12) (that characterize the dependence of the resonant quadratic interaction coefficient on the mode wavevectors [18]), can promote the instability [18, 16], Results of the numerical simulations of eq.(5) that show the transition from hexagonal arrays of dots or pits to stripe patterns ( wires ) with the increase of the supercrificality are shown in Fig.9. Transition from dots to wires in epitaxially strained films has been observed in experiments [19],... 

A.A.Golovin, S.H.Davis and P.W.Voorhees, Self-Organization of Quantum Dots in Epitaxially-Strained Solid Films , Phys. Rev. E 68, 056203 (2003). 

Third, and finally, it has been established that the lanthanide magnetism is in general remarkably robust, and in particular is insensitive to the interfaces, even in crystals only a few atomic layers thick. A reservation of critical importance in this regard is the central role of the state of strain in the description of the magnetic behavior. Specifically it has been established for Dy that epitaxial strains 2% are sufficient to double the Curie temperature or completely suppress the ferromagnetic phase. The twin assets of robustness and strain sensitivity make these materials at one time both ideal systems with which to explore epitaxial effects, and attractive models with which new states of magnetic order may be designed and synthesized. 

Spencer, B. J., Voorhees, P. W. and Davis, S. H. (1991), Morphological instability in epitaxially strained dislocation free solid films. Physical Review Letters 67, 3696-3699. 

Donner, W., Chen, C., Liu, M., Jacobson, J Lee, Y.-L., Cadre, M., and Morgan, D. (2011) Epitaxial strain-induced chemical ordering in Lao.sSro.sCoOs-a films on SrTiOs. Chem. Mater., 23, 984-988. 

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